Constructor Function
The Constructor Function is an uncomputable function. Definition: \(C(0)=0\) (null program) \(C(n)=\text{Largest returned value of JavaScript (ECMAScript 7) program of length } n\) doesn't count. The final value calculated by the program is the return value, similar to if the code was run using the function. The old definition of this function can be approximated by C^n(n). C^1(1)=9 C^2(2)=9^9^(9E99) C^3(3)>BB(BB(9E9)) C^x(x) is at least BB(BB(BB(...(x)...))) with x BBs According to User:Cool and good and cool, \(C^4(3)\) is very large, although it won't exceed numbers like Big FOOT and Rayo's Number. The (old) Constructor Function has an Uncomputability Level of 2. \(C(n)\), \(C^{n}(n)\), etc. (all non-oracle extensions) are slower-growing than the FOST Function due to the quantifier \(\exists\). KNOWN VALUES \(C(0)=0\) because the only 0-length program is the null program, which (in a way) returns 0. \(C^1(1)=9\) using . \(C^2(2)\geq9^{9^{9E99}}=9^{9^{9*10^{99}}}\), using (most likely the largest). \(C^3(3)\) is probably much larger than \(BB(10^{10^{80}})\) using a Turing Machine emulator. This is because the Busy Beaver machine for a very large number of states could be stored in some sort of compressed state, which is decompressed repeatedly and run. FE OLD EXTENSION TO THIS THING So suppose we have JS program working with set theory now lets call perm1 as language that can describe anything in this language with 1 symbol. Sol it have all permutations as the number of symbols, e.g. If it was 1 and 2 language and 2 symbols length perm1 would have 1 symbol for 1 for 2 for 12 for 11 for 21 for 22 eg 1 is still 1 (we dont need new symbol), and 2, q 1 is 12, w is 11, e is 21, r is 22 so largest number with permC(C...(C(999))...) WITH C(C(C(999))) C'S language WRITTEN WITH C(C(C(999))) SYMBOLS = PRETTYNUMBER Extension by User:Maxywaxy 1 Constructor2 Function CC(x,1) = largest possible return value using ONLY CONSTRUCTOR FUNCTION and x characters in base 10. superscript symbol ^ (indicating repetition) does not count as a character, but parentheses do values for CC(x,1) # 9 # 99 # 999 # C(9) # C9(9) # C99(9) # C999(9) # CC(9)(9) and so on. CC(x,2) = CC in the same way normal C progresses. CC(1,2) = 9 CC(n,2) = CC(n-1,2)+1 ... y=1 and y=2 is like 2-argument constructor do it like that CC(10,10) = duostructen Extension by User:Maxywaxy 2 Super Constructor function \(SC(0)\) = \(C(10^{100})\) \(SC(n+1)\) = \(C^{SC(n)}(SC(n))\) example: \(SC(1)\) = \(C^{C(10^{100})}(C(10^{100}))\) It is sort of a salad function \(SC(10^{100})\) = Superstructor C.U.M.A.N TOP-SECRET THING FOR UNKNOWN GOALS... #\ Extension by User:Naruyoko My extension is something. This is totally not stolen idea from \(\Sigma_2\) and \(\Xi\). In \(C_2\), there is a unary function, say, , hardcoded so you wouldn't have to import it or anything, that acts as an oracle for the halting problem of a JavaScript program as string. The string is solved as(for example, variables) it would interact in , but it won't mutate variables. However, it can not solve the halting problem that includes . Similarly, we can define \(C_3\) with unary function, say, , that solves halting problem of JavaScript+ , but not JavaScript+ . Then \(C_4\) and so on. The unary oracle always has 1 byte name. \(C_2(n)\) is known to grow at least as fast as Rayo's FOST Function. One of the reasons that this function grows so quickly compared to other "Kolmogorov functions" is that JS is weakly typed, as well as how flexible the language is, and how easy it is to compress and eval() source code in JS. For any of those, there is binary operator, named for any of those, which takes JavaScript program first, and then an integer which indicates it is oracle of JavaScript+ . The maximum value of is one less than the subscript of this extension of \(C\). I don't know the strength, but it may reach \(\omega_\omega^\text{CK}\). \(C_n(n)\) grows at a similar rate to \(R_n(n)\) using the Rayo Hierarchy. Category:FUNCTIONS Category:POTENTIALLY WELL-DEFINED Category:Uncomputable Functions Category:C7X's Stuff Category:Computer Science Related Functions Category:Uncomputability Level \(\ge 2\) Category:NOTATIONS WITH SOME SECRET EXTENSIONS